Dear Statalist community,

I am running the following code to initially generate a regression output:
Code:
xtreg y c.a##c.b $controlvariables i.fyear, fe
This code generates the following with control variables and year output omitted for simplicity:
Code:
Fixed-effects (within) regression               Number of obs     =     11,363
Group variable: gvkey                           Number of groups  =      1,547

R-squared:                                      Obs per group:
     Within  = 0.4145                                         min =          1
     Between = 0.3950                                         avg =        7.3
     Overall = 0.4009                                         max =         12

                                                F(24,9792)        =     288.80
corr(u_i, Xb) = -0.4448                         Prob > F          =     0.0000

-------------------------------------------------------------------------------------
                  y | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------------+----------------------------------------------------------------
                  a |  -.8820247    1.37278    -0.64   0.521    -3.572956    1.808907
                  b |  -.1120089    .110937    -1.01   0.313    -.3294683    .1054504
                    |
            c.a#c.b |   6.042615   2.489008     2.43   0.015     1.163646    10.92158
                    
  
              _cons |     13.749   1.191463    11.54   0.000     11.41348    16.08451
--------------------+----------------------------------------------------------------
            sigma_u |  4.8700768
            sigma_e |  2.9240485
                rho |  .73502736   (fraction of variance due to u_i)
-------------------------------------------------------------------------------------
F test that all u_i=0: F(1546, 9792) = 2.86                  Prob > F = 0.0000

Then, i run some post-estimation commands to generate an interaction plot.

margins, at(b=(0(1)1) a =(0 1))

Predictive margins Number of obs = 11,363
Model VCE: Conventional

Expression: Linear prediction, predict()
1._at: a = 0
b = 0
2._at: a = 0
b = 1
3._at: a = 1
b = 0
4._at: a = 1
b = 1

------------------------------------------------------------------------------
| Delta-method
| Margin std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
_at |
1 | 9.605668 .028179 340.88 0.000 9.550438 9.660898
2 | 9.493659 .1150657 82.51 0.000 9.268134 9.719184
3 | 8.723643 1.379275 6.32 0.000 6.020313 11.42697
4 | 14.65425 2.704182 5.42 0.000 9.354149 19.95435
------------------------------------------------------------------------------

marginsplot
Above margins code generates the following marginsplot
Please see attached for graph

I have the following questions!

1. The regression output shows coefficient of 13.749. In the margins command output, I was expecting the 13.749 to match where a =0 and b = 0 where the main standalone variables are zero. However, this does not seem to be true also in the marginsplot as well. Would this be because i am including control variables as well as fixed effects?

2. Based on the regression output, the effect of a depends on the value(s) b but not by themselves. I am having a little bit of trouble understanding the economic magnitude of the coefficients. Can I add the interaction coefficient to the intercept as the total effect?

3. If the interpretation in #2 is correct, then can I graph this out somehow where I can show the interaction term's 6.04 coefficient in the graph? In other words, if the intercept of 13.749 "increases" by 6.04 (interaction term coefficient), can this increase be visualized in Stata?

Thank you so much,